For step 2: This means that $106 \%$ of the cost of the cooler is the total bill, $ \$7.95$. Now you can solve for the missing variable. (Divide the percent by 100 to get it in fraction form first.)
$(106 / 100) \times 1=\$7.95$
Answer (2)
The original cost of the cooler before tax was added is $7.50. We found this by defining the cost as x , setting up the equation 1.06 × x = 7.95 , and solving for x . Dividing $7.95 by 1.06 gives us the original price.
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Define the variable: Let x represent the original cost of the cooler.
Set up the equation: 1.06 × x = 7.95 .
Solve for x by dividing both sides by 1.06 : x = 1.06 7.95 .
Calculate the result: x = 7.5 . The original cost of the cooler is $7.50 .
Explanation
Understanding the Problem The problem states that 106% of the cost of a cooler is $7.95 . We need to find the original cost of the cooler before the sales tax was added.
Setting up the Equation Let x be the original cost of the cooler. The problem tells us that 106% of x is equal to $7.95 . We can write this as an equation: 1.06 × x = 7.95
Isolating the Variable To solve for x , we need to divide both sides of the equation by 1.06 : x = 1.06 7.95
Calculating the Original Cost Now, we perform the division: x = 7.5 So, the original cost of the cooler is $7.50 .
Examples
Imagine you are buying an item online, and the price shown includes sales tax. If you want to know the original price of the item before tax, you can use this method. For example, if the total price is $10.60 and the sales tax is 6% , you can calculate the original price by dividing $10.60 by 1.06 , which gives you $10 . This is useful for budgeting and comparing prices.
